Dr Rowan Williams said they needed to be more concerned with providing places to disadvantaged children than “securing our membership”.

In an address to the General Synod, the Church’s parliament, on Saturday, the archbishop said that its schools need to be “open for as many children as possible”.

His comments come as the Church launches new advice on admissions policies which attempts to break the middle-class stranglehold on its most popular schools by calling for an end to the “points system” which benefits families most involved in the church.

Referring to the new guidelines, he conceded that the Church faces a challenge in maintaining the core values of its schools at a time of “startlingly far-reaching” changes.

“How, in the context of far-reaching changes to how education is delivered in this country, do we continue to offer what we have always offered?” he said.

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“Which is not a system of confessional schools designed to secure our membership, but a critical partnership with the state that seeks to keep open for as many children as possible the fullest range imaginable of educational enrichment.

“Our history as educators in this country is much to do with offering possibilities in social contexts where other providers have practically given up or have settled for less than the best.”